More than a third of the investors voting at the generic drugmaker's annual meeting last week cast votes against Coury, while over half voted against Cameron - who heads Mylan's compensation committee, a letter reviewed by Reuters shows.
"We believe Mylan's independent directors must act swiftly - or risk further erosion in shareowner confidence and value," the investors wrote in the letter to Mylan's independent directors.
"Mylan's share price is already down nearly 50 percent since its April 2015 peak and the company remains under legal, regulatory and public scrutiny for its EpiPen pricing practices," they added in the letter.
Mylan could not be immediately reached for comment.
The company has been grappling with a growing backlash from U.S. consumers over the price of its life-saving allergy treatment EpiPen after it shot up to more than $600 for a two-pack of the device from less than $100 in 2007. [nL2N1HB1KX]
While the sharp price spike spurred congressional, Justice Department and other government investigations, the shareholder campaign against Mylan's board picked up steam after Chairman Coury's nearly $100 million pay package was disclosed earlier this year. [nL1N1J41AU]
The investor group, including New York City and State pension funds and the California teachers pension fund, have asked for Coury to forfeit most of the pay he received last year. It also urged Mylan to hire an independent chairman and reconstitute its board with a majority of independent directors.
The investors agitating against Mylan's board had a steep threshold to cross as more than two-thirds of the shares voted, as well as more than half of Mylan's outstanding shares, would have needed to be cast against the directors for them to lose.
Neil Dimick and Mark Parrish, directors on the company's compensation committee, had just under 50 percent of the shares voted cast against their re-election.
Investors also cast more than a quarter of the shares voted against Chief Executive Heather Bresch.
Mylan announced the vote totals from the meeting in a filing with regulators on Wednesday. The company had previously only said that all its directors had been re-elected.
More than 80 percent of the company's shares voted were cast against the company's 2016 executive pay packages. That vote was a non-binding, advisory measure.
New York City comptroller Scott Stringer, who oversees the city's pensions and is one of the leaders of the campaign against the drugmaker's board, said the board needed to act swiftly to restore investor confidence.
"This board's oversight failures have hurt investors, consumers and American taxpayers. We need to see change," Stringer said in a statement.
(Reporting by Michael Erman; Editing by Sandra Maler and Himani Sarkar)
By Michael Erman